Daily Practice · Higher Plus
September 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2005 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2005On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 2nd September 2005Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 3rd September 2005Make x the subject of 7x + 8 = y(x + 8).
- 4th September 2005A train slows steadily from 14 m/s to rest in 5 seconds. Work out its deceleration.
- 5th September 2005A cuboid measures 12 cm by 10 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th September 2005A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th September 2005A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 8th September 2005Simplify sqrt(80) + sqrt(245), giving your answer in the form a sqrt(b).
- 9th September 2005Write 3/(x + 4) + 6/(x + 5) as a single fraction.
- 10th September 2005y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 11th September 2005The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 12th September 2005A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 13th September 2005On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 14th September 2005A rectangle is 15 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th September 2005Solve 12x^2 + 23x + 5 = 0.
- 16th September 2005y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 17th September 2005In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 18th September 2005The probability of winning a game is 3/4. A player expects 24 wins. How many games did they play?
- 19th September 2005A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
- 20th September 2005Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 21st September 2005f(x) = 5x - 1. Work out the inverse function f^-1(x).
- 22nd September 2005y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 9.
- 23rd September 2005In a vector proof you find that vector PQ = 4a + 3b and vector RS = 8a + 6b. What does this show about PQ and RS?
- 24th September 2005A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 25th September 2005On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th September 2005A block has mass 220 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th September 2005Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 28th September 2005A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 29th September 2005A cuboid measures 7 cm by 8 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th September 2005A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?